The England centre-half suffered soft tissue damage to his hamstring during his side’s 1-0 defeat to Sunderland on Thursday.
As a result, Jagielka missed Sunday's 2-1 victory over Southampton, with Antolin Alcaraz deputising in the Everton backline.
After the game, Martinez said: "With this soft tissue injury it could be up to four weeks, but knowing Jags he will be back earlier.
"It is just the accumulation of games and the demands of this month - November into December is high-risk in terms of injuries to the players.
"When you have the number of games we play, it is understandable."
‘Even though it was late in the game, the Arsenal fans started singing my name. It felt like the moment I announced myself as a professional footballer’: Ex-Gunners star recalls scoring first senior goal as a teenager at Highbury
'I started to drive myself crazy': Former Manchester United midfielder explains why it all went wrong for him under Erik ten Hag
